From: A rational cubic trigonometric approximation scheme of the generalized Cornu spirals
Approximation schemes | Values of parameters/anticipated tolerance (\( \varepsilon \)) | Circular arc | Cornu spiral | Logarithmic spiral | Non-inflecting GCS | Normalized GCS |
---|---|---|---|---|---|---|
G 2-approximation | \( d_{1} \) | 0.5 | 1.515 | 5 | 1.1 | 2 |
d 3 | 0.5 | 1.426 | 1.7 | 1.1 | 2 | |
\( \varepsilon \) | 3.59 × 10−2 | 2.78 × 10−2 | 6.42 × 10−2 | 1.10 × 10−2 | 0.05 | |
G 1-approximation | \( d_{1} \) | 0.457 | 1.45 | 2.28 | 1.089 | 2 |
d 3 | 0.688 | 1.40 | 3.19 | 0.899 | 2 | |
μ 1 | 0.876 | 0.67 | 0.88 | 1.55 | 0.8 | |
μ 2 | 0.812 | 0.899 | 0.787 | 1.32 | 0.8 | |
\( \varepsilon \) | 3.59 × 10−2 | 2.78 × 10−2 | 6.42 × 10−2 | 1.10 × 10−2 | 0.05 |